On the Skew Cyclic Codes and the Reversibility Problem for DNA 4-Bases

Abstract

The DNA 4-bases are matched with the 256 elements of the finite ring R= F<inf>4</inf>+ uF<inf>4</inf>+ vF<inf>4</inf>+ uvF<inf>4</inf>, where u2= u, v2= v, uv= vu. By defining a non trivial automorphism over R, the skew cyclic codes over the finite ring R are introduced. The reversible DNA codes are obtained, by using the skew cyclic codes whose generator polynomials satisfy some conditions. Thanks to this, the reversibility problem for DNA 4-bases can be solved. Moreover, the Gray images of the skew cyclic codes over the finite ring are determined. © 2019, Springer Nature Switzerland AG.